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 An Identity Problem (Posted on 2006-08-17)
Four inhabitants of the island make the statements as given below. Each of these inhabitants are either Liars or Knights. Little is known regarding the identity of the four inhabitants except for the fact that Q and R are not both Knights.

P's Statement: If asked, Q would say that he and S belong to the same group.

Q's Statement: If asked, S would say that he and P do not belong to the same group.

R's Statement: P and myself belong to the same group..

S's Statement: If asked, P would say that he and R do not belong to the same group.

To what group or groups do the four speakers belong?

 See The Solution Submitted by K Sengupta Rating: 3.5000 (2 votes)

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 Quick | Comment 3 of 11 |
If Q and R are not both knights, at least one of them is a liar.

Assume R is a liar. From what he says, it follows that P is a knight. What S says is true, so S is a knight. And Q is lying, so he is a liar.

Thus, if there is just ONE solution, P and S are knights, and Q and R are liars.

 Posted by Federico Kereki on 2006-08-17 18:00:08

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